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1 INTRODUCTION
In recent years a dynamically growing interest in
autonomous vehicles can be observed both in
academia and industry. Starting from self-driving
cars, through autonomous mobile robots and
autonomous drones, and reaching out to autonomous
ships. The last group recently obtained a specific term
expressing such vehicles, which was introduced by
the International Maritime Organization (IMO).
Autonomous vessels are referred to as Maritime
Autonomous Surface Ships (MASS) and this term
became very popular nowadays and is commonly
used by researchers, classification societies,
equipment manufacturers and technology providers.
According to the American Bureau of Shipping (ABS)
“an autonomous ship is a marine vessel with sensors,
automated navigation, propulsion and auxiliary
systems, with the decision logic to follow mission
plans, sense the environment, adjust mission
execution for the environment, and operate without
human intervention.” [1]
Bureau Veritas categorizes ship autonomy levels in
a 5-points scale from 0 to 4. Level 0 is a conventional,
fully manned ship, where staff make and execute
decisions based upon acquired data. Level 1 is a smart
ship, which is defined as a vessel guided by humans,
which uses sensors and systems for data acquisition
and support in decision making. Levels 2 and 3 are
semi-autonomous ships. Their operation is supervised
by humans, but relies on decision making systems.
Level 4 is a fully autonomous ship, which is an
unmanned ship that does not need any human
intervention other than in an emergency. [4]
Further details on ship autonomy levels and
autonomous vessels classification can be found in [2]
and [21].
In the last decade many research projects on the
development of autonomous ships technology were
carried out. Among them are: Maritime Unmanned
Navigation through Intelligence in Networks
(MUNIN) [22], ReVolt [5], Advanced Autonomous
Waterborne Applications (AAWA) [26], Autosea [25],
Autoferry [24], Yara Birkeland [11] and Safer Vessel
with Autonomous Navigation (SVAN) [27].
Verification of a Deterministic Ship's Safe Trajectory
Planning Algorithm from Different Ships’ Perspectives
and with Changing Strategies of Target
Ships
A
. Lazarowska
Gdynia Maritime University, Gdynia, Poland
ABSTRACT: The paper presents results of a ship's safe trajectory planning method verification - the Trajectory
Base Algorithm, which is a deterministic approach for real-time path-planning with collision avoidance. The
paper presents results of the algorithm’s verification from different ships’ perspectives and with changing
strategies of target ships. Results prove the applicability of the algorithm in the Collision Avoidance Module of
the Autonomous Navigation System for Maritime Autonomous Surface Ships.
http://www.transnav.eu
the
International Journal
on Marine Navigation
and Safety of Sea Transportation
Volume 15
Number 3
September 2021
DOI: 10.12716/1001.15.03.17
624
In table 1 research projects on autonomous ships
are listed in a chronological order from the oldest to
the newest.
Table 1. Research projects on autonomous ships
_______________________________________________
Project Type of vessel Years
_______________________________________________
MUNIN [22] not specified 2012-2015
ReVolt [5] 60 m, 1300 DWT, battery 2013
powered
AAWA [26] not specified 2015-2018
Autosea [25] not specified 2015-2019
Autoferry 5 m, electric passenger ferry 2016-2019
[24] milliAmpère
Yara 79.5 m, fully electric container 2017-2022
Birkeland [11] feeder, 120 TEU
SVAN [27] 53.8 m, ferry Finferries Falco 2018
_______________________________________________
According to [2] Autonomous Surface Vehicles
(ASVs) are divided into Maritime Autonomous
Surface Ships (MASS) and Unmanned Surface
Vehicles (USVs), which are small crafts without a
crew onboard, that can be controlled remotely or can
operate fully autonomously. Development projects
are also conducted in relation to USVs. Table 2
presents examples of recently developed USVs.
Table 2. Recently developed USVs
_______________________________________________
USV Country Length [m] Speed
_______________________________________________
Katana [7] Israel 11.9 60 kn
Tianxing-1 [33] China 12.2 over 50 kn
C-Target 9 [15] USA 9.6 50 kn
Edredon [8, 10] Poland 5.7 30 kn
_______________________________________________
2 AUTONOMOUS NAVIGATION SYSTEM
According to the European Maritime Safety Agency
(EMSA) [6] in the years 2014–2019 19418 marine
casualties and incidents were reported in the
European Marine Casualty Information Platform
(EMCIP). During 833 safety investigations carried out
in the years 2014–2019, 1801 accident events were
distinguished and analyzed. 54% (969) of these
accident events were categorized as human actions
and 28% as system/equipment failures. Collisions
(1769), contacts (2268) and grounding/stranding
(1765) represent 44% of all casualty events that took
place in the analyzed period of time. 78 fatalities were
reported in collisions that occurred in the years 2014–
2019. According to the results of an investigation
presented in [35] application of unmanned ships
should cause the reduction of groundings and
collisions. Therefore, the introduction of autonomous
vessels might be regarded as a desired phenomenon,
which will contribute to the increase of safety at sea.
Collision avoidance is one of the most important
tasks that has to be performed during ship navigation.
That is true not only for conventional ships, but it
equally applies to autonomous vessels. In order to
better understand the importance of collision
avoidance and safe trajectory planning algorithms for
a proper functioning of an autonomous ship, a brief
overview of recent concepts on Autonomous
Navigation Systems (ANSs) will be described below.
The ANS is a system responsible for the navigation
of an unmanned vessel. Table 3 shows an analysis of
the ANSs applied in recent projects on autonomous
ships. In the MUNIN project the ANS is composed of
two subsystems, responsible for weather routing and
collision avoidance. An important system providing
input data to the ANS is the Advanced Sensor Module
(ASM) [23]. In the AAWA project the ANS is
composed of four modules: Route Planning (RP),
Situation Awareness (SA), Collision Avoidance (CA)
and Ship State Definition (SSD) [26]. The CA module
is responsible for the collision risk assessment, based
upon data obtained from the SA module. The second
task of the CA module is an assurance of safe
navigation of the ship, both in the open sea and in
restricted waters. The SA module, which is an analogy
to the ASM in the MUNIN project, fuses data from
different navigational sensors. In the Autosea project
the CA module is composed of: Collision Detection,
Collision Avoidance and Guidance subsystems [3, 14].
Input data are acquired from the Sensor Fusion
Module, which gathers data from different
navigational sensors and systems, such as
navigational charts, AIS and radar. To sum up,
despite the difference in the nomenclature used in the
projects, the functions of modules for collision
avoidance and data fusion are identical or very
similar, with very slight difference in their design and
operation.
The main component of the CA module of the
ANS is a collision avoidance algorithm, responsible
for the determination of a safe maneuver or a safe
trajectory of unmanned vessel, when a collision risk
has been detected. Table 4 lists the collision avoidance
algorithms applied in recent projects on autonomous
ships. Table 5 lists other recent most promising
collision avoidance methods for ships, applicable also
to unmanned and fully autonomous vessels.
Table 3. ANSs in research projects on autonomous ships
_______________________________________________
Project Module for Module for Data
collision data sensors
avoidance reception
and fusion
_______________________________________________
MUNIN Collision Advanced marine radar,
[23] Avoidance Sensor AIS receiver,
(CA) module Module daylight &
(ASM) infrared cameras,
nautical data
AAWA Collision Situation visual cameras, IR
[26] Avoidance Awareness cameras, radar,
(CA) module (SA) module lidar
Autosea Collision Sensor AIS, radar, camera,
[3, 14] Avoidance Fusion charts
(CA) module Module
_______________________________________________
Table 4. CA algorithms in research projects on autonomous
ships
_______________________________________________
Project Collision avoidance algorithm
_______________________________________________
MUNIN [23] Based upon formalized description of
COLREGs
AAWA [26] Velocity Obstacles (VO) method
Autosea [3, 14] Model Predictive Control (MPC)
_______________________________________________
625
Table 5. Recent CA algorithms
_______________________________________________
Author Year Collision avoidance
algorithm
_______________________________________________
Kang Y. et al. [9] 2021 Differential Evolution (DE)
algorithm
Zhang W. et al. [34] 2021 Velocity Obstacles (VO)
Koszelew J. 2020 Beam Search Algorithm (BSA)
et al. [12]
Lazarowska A. [16] 2020 Discrete Artificial Potential Field
(DAPF)
Lisowski J. [18, 19] 2020 game theory
Kuczkowski Ł. and 2017 Evolutionary Algorithm (EA)
Śmierzchalski R. [13]
Lazarowska A. [17] 2017 Trajectory Base Algorithm (TBA)
Mohamed-Seghir 2017 fuzzy sets
M. [19, 20]
Szłapczyńska J. and 2017 heuristic method based on
Szłapczyński R. [28] Collision Threat
Parameters Area (CTPA)
Tam Ch. and 2013 deterministic method
Bucknall R. [31]
Szłapczyński R. 2012 Evolutionary Algorithm (EA)
and Szłapczyńska J.
[29, 30]
Tam Ch. and 2010 Evolutionary Algorithm (EA)
Bucknall R. [32]
_______________________________________________
In order to validate the ship’s trajectory planning
algorithm a number of simulation tests is performed
and results of these experiments are evaluated.
Solutions are assessed in terms of their safety,
compliance with COLREGs, efficiency, which is
evaluated by one or a few of the following criteria:
path length, time of passage, number and value of
course alteration maneuvers, deviation from the initial
course. A complex validation of a collision avoidance
algorithm for ships should include also tests assessing
solutions from different ships’ perspectives and with
changing strategies of target ships. Results of
algorithms’ evaluation including these two above
mentioned criteria are not commonly presented in the
literature. Examples of an algorithm’s assessment
from the perspectives of different ships taking part in
considered situation can be found in [9, 29–32].
Changing strategies of target ships are regarded in an
approach based upon an evolutionary algorithm,
introduced in [13]. Another example is the game
theory approach, presented in [18, 19], which in its
operation principle includes changing strategies of
dynamic obstacles. As stated in [18] games can be a
cooperative or non-cooperative interaction between
players (ships).
This paper presents results of an evaluation of a
deterministic algorithm for ship’s trajectory planning,
called the Trajectory Base Algorithm (TBA).
Assessment of the algorithm was concentrated on the
two above mentioned aspects: compliance of
trajectories from different ships’ perspectives and the
algorithm’s behavior considering changing strategies
of target ships.
The rest of the paper is organized as follows. In
section 3 the tested algorithm is briefly introduced.
Section 4 presented results of simulation tests, in the
first part from different perspectives of ships and in
the second part with changing strategies of dynamic
obstacles. Section 5 presents conclusions resulting
from the presented outcomes.
3 THE METHOD DESCRIPTION
Applied algorithm is a deterministic approach. The
advantage of such algorithm is the certainty of
achievement an identical solution for every run of
calculations with the same input data as there is a lack
of stochastic mechanisms in the algorithm’s operation.
Simplicity of the approach contributes to the
achievement of relatively low run time of the
algorithm what makes the approach applicable in
practical applications of real time path planning in
Collision Avoidance Modules of Autonomous
Navigation Systems for unmanned and fully
autonomous ships.
Input: Ψ, V, Ψ
j
, V
j
, D
j
, N
j
, positions_of_static_obstacles
for (t = 1; t <= t_max; t++) do
candidate_path = path(t);
divide candidate_path into k steps
for (step = 1; step <= k; step++) do
collision check procedure
if (collision == true) then
reject candidate_path
break;
end if
end for
if (collision == false) then
break;
end if
end for
if (collision == false) then
solution_found
Output: path_length, transition_time, ΔΨ
else
Output: lack_of_solution
end if
Figure 1. Pseudocode of the TBA.
The operation principle of the Trajectory Base
Algorithm (TBA) for ship’s collision avoidance is
based upon the search through a base of trajectories.
Stored trajectories constitute candidate solutions. A
solution to the problem is the best collision-free
trajectory with the minimal path length. Trajectories
are evaluated by the division into a number of steps.
In every step an own ship is moved into a new
instantaneous position along the evaluated trajectory
and target ships, modeled with the use of ship
domains are moved into corresponding instantaneous
positions resulting from their motion parameters.
After that the algorithm checks, whether their current
instantaneous positions do not cause a collision. When
an evaluated own ship trajectory does not cause a
collision with any of the target ships during an own
ship’s movement along it, then it becomes the final
solutions and further calculations are terminated. The
reason for that is the order of trajectories in the base,
which are sorted according to the increasing length.
The COLREGs fulfillment is achieved by a proper
shape and size of applied ship domain. The ship
domain size also takes into account the conditions of
good and restricted visibility at sea. A ship domain
applied in presented simulation tests is a hexagon
domain with the following dimensions: distance
towards the bow = 1.3 nm, distance of amidships = 0.6
nm, distance towards the starboard side = 0.6 nm,
distance towards the stern = 0.5 nm and distance
towards the port side = 0.5 nm, suitable for good
626
visibility conditions. Figure 1 presents a pseudocode
of the TBA. A more detailed description of the TBA
can be found in [17].
4 SIMULATION EXPERIMENTS
The TBA was implemented in the MATLAB
programming language and tested with the use of a
number of test cases. Examples of obtained solutions
were chosen for the presentation in this paper.
Simulation experiments, as it was mentioned above,
were concentrated on the evaluation of solutions’
consistency from the perspectives of different ships
taking part in the considered test case. In the second
part of experiments the algorithm was tested
including changing strategies of target ships. The
changes of target ships strategies covered course
alterations. Calculations were carried out using a PC
with Intel Core i7-10750H 2.60 GHz, 32 GB RAM, 64-
bit Windows 10 operating system.
4.1 Different perspectives
In the first part of experiments different test cases
were evaluated from the perspectives of all ships
taking part in an encounter situation. Solutions of a
few test cases chosen for the presentation in the paper
are shown in Figures 2-4. The scales in figures are in
nautical miles. An own ship trajectory is marked with
OS abbreviation and target ships’ trajectories are
analogously marked with TS abbreviation followed by
the number of the ship if more vessels take part in the
situation. Consecutive positions of OS and TSs in
figures are marked with numbers indicating the
corresponding time in minutes (rounded to integers).
Analysis of these results enables to state that
trajectories calculated by the TBA for all of the ships
participating in the considered encounter situation are
compliant and do not lead to a collision between any
of the vessels.
4.2 Changing strategies
In the first part of simulation experiments the
algorithm was evaluated in terms of its performance
for situations with changing strategies of target ships.
An example of such test case is presented in Figure 5,
where the target ship alters its course during its
movement along an initial trajectory. As it can be seen
in Figure 5 a trajectory calculated by the algorithm for
an OS constitutes a safe trajectory. Obtained results
lead to the conclusion that the algorithm assures
calculation of a safe solution also with regard to
situations of changing strategy of a target ship.
An analysis of performed simulation tests enable
to state the following conclusions. The algorithm
calculates compliant solutions from the perspectives
of different ships taking part in the considered
encounter situation. Calculated solutions are
compliant with COLREGs (are large enough to be
readily apparent for other vessels (rule 8b) and are
performed to the proper side of the vessel (rules 13, 14
and 15).
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Figure 2. Solutions returned by TBA from both ships’
perspectives for test case 1 (head-on scenario, good
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Figure 3. Solutions returned by TBA from both ships’
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visibility).
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Figure 4. Solutions returned by TBA from all ships’
perspectives for test case 3 (with 2 target ships, good
visibility).
627
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Figure 5. Solution returned by TBA for test case 4 (changing
strategy of the target ship, good visibility).
5 CONCLUSIONS
The paper presents results of complex simulation
experiments with regard to an algorithm for ship’s
real-time path-planning with collision avoidance. The
Trajectory Base Algorithm, to which these studies
relate, is a deterministic approach developed by the
author of the paper and introduced in previous
works. This paper presents results of extended tests of
this algorithm including verification from different
ships’ perspectives and with changing strategies of
target ships. Results constitute the next step of
validation of this approach in terms of its applicability
in the Collision Avoidance Module of the
Autonomous Navigation System for Maritime
Autonomous Surface Ships. Obtained solutions prove
a successful validation of the method with the use of
above described tests. It is planned to test the
algorithm in real life operating conditions onboard a
ship with input data from ARPA and AIS fed into the
algorithm in real time. Preliminary real-life tests of the
algorithm have already been performed, but more
extensive testing is still needed before commercial
application can be regarded.
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